I don't think most English words have Latin or Greek roots.
French probably has a slightly more sizable amount of loanwords in English than Latin, and is much more sizable than Greek. The reason why Latin, French, and Greek to a lesser extent make up so much is that:
1) at the time English started being a written language again (1200-1500) most academic texts were written in Latin, French or Greek.
2) in 1066 the Normans successfully conquered England. Most of the courts and upper classes spoke French. French and Latin were the languages of government.
3) Greek was one of the first languages Christians spoke as they entered Europe. Many ancient religious texts were written in Greek, so Greek theological concepts entered many languages where the majority of speakers were Christian. Latin was also an ecclesial language, and priests probably made up the majority of literate people in the middle ages.
4) As universities shifted from primarily theology~philosophy, to more philosophy~natural science~history (and eventually incorporated social sciences), professors in the English speaking world still taught classes in Latin. Until the 20th century, Latin was a compulsory subject for many native English speakers who wanted to learn. Scientific papers were still frequently being published in Latin. Most of Isaac Newton's work was written in Latin, despite the fact he was at the University of Cambridge.
5) English speakers have no problems borrowing words. It is almost a faux pas to "make up" a word using English roots. Native speakers criticize each other for doing so, but then if you say a word from another language instead and the listener doesn't understand it, the listener feels less educated. This pattern has been happening for centuries in English.
"Are westerners the one who formed entire dictionary? Please share the possible reasons for this."
What? I don't know how to answer that. Dictionaries are just attempts to document the words in a language and provide spelling, context, and a definition.
"Are other languages not as rich as these two or there is some hidden truth behind this?"
No, plenty of languages don't borrow heavily from Latin and Greek. German is one, Polish is another. A lot of psychology research was originally written in German and people did not have any trouble expressing themselves without high amounts Latin and Greek roots.
I've recently started following a podcast that has discussed this. The Spoken History of a Global Language. You can browse the episodes here - The History of English Podcast. They go into great detail about how English evolved.
Others have mentioned the Norman Conquest, which certainly contributed a lot, but we can see Latin and Greek influences before that as well. Here are a few examples.
Why do most English words have Latin or Greek roots?
All three are descendents of proto Indo European languages. An old Quora post shows a tree diagram. The influence of Latin is supposed to be from Norman French on middle English. The Catholic church used Latin. You can read about the Latin influence on English here. As we can see from the tree diagram of the old Quora post, despite belonging to proto Indo European, are not close or directly related. So their influence has been indirect. The article here shows the sources of Greek words that came into English.
Edit : Adding another source discussing the same kind of question.